In the many fields of physical science in which researchers deal with aspects of radiative transfer, one important task is to determine the direction and intensity of radiant energy transport within a region of interest, given: 1) optical parameters describing the scattering and absorption characteristics of the optical media within the region; 2) the specification of the direction and intensity of radiant energy incident on the boundary of the region; and 3) the specification of any radiant source distribution within the region. For example, the development of optical coherence tomography techniques in the realm of medical optics requires knowledge of the response of new optical instruments.
Accurate calibration of blackbody sources used in pyrometry and spectroscopy requires determination of the emission characteristics of new experimental sources. Remote sensing of the earth's atmosphere, terrain and marine environments depends upon instruments, the design and calibration of which are possible only after the specification of the optical conditions in which the instruments are to perform. These specifications are frequently determined by simulation of the radiant energy transport in the physical conditions to be encountered by the instruments.
The process common to all three endeavors mentioned above, namely, the radiative transfer of energy through media capable of interacting with and altering the radiance field, is governed by the Radiative Transfer Equation or RTE. Unfortunately, the RTE supplies no analytic solution for problems characterized by realistic geometries, boundary conditions and optical parameters. As a result, the “solving” of the RTE for realistic optical environments consists currently of specifying the parameters necessary to define the problem, and then numerically simulating the solution, such as the radiance field, at the desired location(s).
Many methods for generating numerical solutions to the RTE in the optically coupled ocean-atmosphere environment have been developed in support of studies of the earth's atmosphere and oceans. Most of this environment can be represented by one-dimensional models that treat the atmosphere and oceans as stratified media that are horizontally infinite in extent and in which the optical parameters vary only with depth or height. Indeed, in the common case of clear sky over open ocean waters, the one-dimensional approximation is very good; the one-dimensional models execute quickly and have negligible or acceptable error. In order to operate effectively, a researcher or other person using monitoring equipment should be capable of establishing parameters for the particular environment and the conditions at the time of taking readings. Because these parameters are dynamic in nature, it is necessary to formulate a scenario for the conditions at the time of the instrumental measurements to determine the effectiveness of the results as well as the set up conditions for the instrumentation. This has been found to be possible in difficult media by using the Monte Carlo method which can give an accurate depiction of the magnitude of the measured entity for a given set of conditions. However, Monte Carlo calculations are also long and cumbersome in nature and require a great amount of data manipulation.